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Three alternative estimators are considered\u2013the Yule-Walker, least-squares, and Burg-type estimates\u2013and a complete analysis of their asymptotic properties in the stationary case is given. The results obtained, when placed together with those found elsewhere in the literature, lead to the direct recommendation that the less familiar Burg-type estimator should be used in practice when modeling stationary series. This is particularly so when the underlying objective of the analysis is to investigate the interrelationships between variables of interest via impulse response functions and dynamic multipliers.<\/jats:p>","DOI":"10.1017\/s0266466600008902","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:41:18Z","timestamp":1236699678000},"page":"884-899","source":"Crossref","is-referenced-by-count":11,"title":["A Note on Autoregressive Modeling"],"prefix":"10.1017","volume":"10","author":[{"given":"D.S.","family":"Poskitt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600008902_ref032","doi-asserted-by":"publisher","DOI":"10.1007\/BF02481980"},{"key":"S0266466600008902_ref029","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347499"},{"key":"S0266466600008902_ref028","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/70.2.389"},{"key":"S0266466600008902_ref027","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1982.tb00350.x"},{"key":"S0266466600008902_ref024","volume-title":"Stationary Random Processes.","author":"Rozanov","year":"1967"},{"key":"S0266466600008902_ref026","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005442"},{"key":"S0266466600008902_ref014","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004722"},{"key":"S0266466600008902_ref015","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.1.200"},{"key":"S0266466600008902_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(89)90059-6"},{"key":"S0266466600008902_ref030","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/50.1-2.129"},{"key":"S0266466600008902_ref003","volume-title":"A Survey of Modern Algebra","author":"Birkhoff","year":"1977"},{"key":"S0266466600008902_ref016","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344208"},{"key":"S0266466600008902_ref007","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1986.tb00484.x"},{"key":"S0266466600008902_ref021","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1111\/j.2517-6161.1985.tb01348.x","article-title":"On the estimation of residual variance and order in autoregressive time series.","author":"Paulsen","year":"1985","journal-title":"Journal of the Royal Statistical Society"},{"key":"S0266466600008902_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02532251"},{"key":"S0266466600008902_ref005","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347635"},{"key":"S0266466600008902_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/2109746"},{"key":"S0266466600008902_ref018","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177698954"},{"key":"S0266466600008902_ref008","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176350836"},{"key":"S0266466600008902_ref031","doi-asserted-by":"publisher","DOI":"10.1029\/JZ070i008p01885"},{"key":"S0266466600008902_ref023","article-title":"Autoregressive approximations and testing for spectral zeroes (invertibility).","author":"Poskitt","year":"1992","journal-title":"Symposium: New Directions in Time Series Analysis."},{"key":"S0266466600008902_ref025","doi-asserted-by":"publisher","DOI":"10.2307\/1912017"},{"key":"S0266466600008902_ref002","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345882"},{"key":"S0266466600008902_ref004","unstructured":"4 Burg J.P. A New Analysis Technique for Time Series Data. Presented at the Advanced Study Institute on Signal Processing, NATO, Enschede, The Netherlands, 1968."},{"key":"S0266466600008902_ref006","volume-title":"The Statistical Theory of Linear Systems.","author":"Hannan","year":"1988"},{"key":"S0266466600008902_ref009","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1946251261"},{"key":"S0266466600008902_ref019","first-page":"389","volume-title":"Multivariate Analysis II","author":"Parzen","year":"1969"},{"key":"S0266466600008902_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(85)90027-2"},{"key":"S0266466600008902_ref011","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600011865"},{"key":"S0266466600008902_ref017","doi-asserted-by":"publisher","DOI":"10.1109\/TGE.1978.294569"},{"key":"S0266466600008902_ref020","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1984.tb00381.x"},{"key":"S0266466600008902_ref022","doi-asserted-by":"publisher","DOI":"10.2307\/2297602"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600008902","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T05:46:22Z","timestamp":1738993582000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600008902\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,12]]},"references-count":32,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1994,12]]}},"alternative-id":["S0266466600008902"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600008902","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,12]]}}}